Year: 2015
Type: article
Abstract: We study the unstable harmonic oscillator and the unstable linear potential in the presence of the point potential, which is the superposition of the Dirac $δ(x)$ and the derivative $δ'(x)$. Using the \textit{physical} boundary conditions for the Green's function we derive for both systems the resonance poles and the resonance wave functions. The matching conditions for the resonance wave functions coincide with those obtained by the self-adjoint extensions of the point potentials and also by the modelling of the $δ'(x)$. We find that, with our definitions, the pure $bδ'(x)$ barrier is semi-transparent \textit{independent} of the value of $b$.
Source: Physica Scripta
Author: F H Maldonado-Villamizar
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G8677342192
OpenAlex ID: W2005699879